99877 ÷ 7 = 14268 R1
No problem, we've got 99877 and 7 for the division.

Step 1:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 9 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 2:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 28 from 29 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 7

Step 3:
7 goes into 18 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 142
Subtract 14 from 18 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 7

Step 4:
7 goes into 47 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 1426
Subtract 42 from 47 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 5:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 14268
Subtract 56 from 57 to get 1.

The final result is 14268 with a remainder of 1.